Page:Elementary Text-book of Physics (Anthony, 1897).djvu/282

268 face is $$4\pi j.$$ This result is of importance in connection with electrical currents.

244. Magnetic Measurements.—It was shown by Gilbert in a work published in 1600, that the earth can be considered as a magnet, having its positive pole toward the south and its negative toward the north. The determination of the magnetic relations of the earth are of importance in navigation and geodesy. The principal magnetic elements are the declination, the dip, and the horizontal intensity.

The declination is the angle between the magnetic meridian, or the direction assumed by the axis of a magnetic needle suspended to move freely m a horizontal plane, and the geographical meridian.

The dip is the angle made with the horizontal by the axis of a magnetic needle suspended so as to turn freely in a vertical plane containing the magnetic meridian.

The horizontal intensity is the strength of the earth's magnetic field resolved along the horizontal line in the plane of the magnetic meridian. A magnet pole of strength $$m$$ in a field in which the horizontal intensity is represented by $$H$$ is urged along this horizontal line with a force equal to $$mH.$$ From this equation the dimensions of the horizontal intensity, and so also of the strength of a magnetic field in any case, are $$[H] = \left[ \frac{MLT^{-2}}{m} \right] = M^{\frac{1}{2}}L^{-\frac{1}{2}}T^{-1}.$$

The horizontal intensity can be measured relatively to some assumed magnet as standard, by allowing the magnet to oscillate freely in the horizontal plane about its centre, and noting the time of oscillation. The relation between the magnetic moment $$M$$ of the magnet and the horizontal intensity $$H$$ is calculated by a formula analogous to that employed in the computation of $$g$$ from observations with the pendulum.

If the magnet be slightly displaced from its position of equilibrium, so as to make small oscillations about its point of suspension, it can be shown, as in § 60, that it is describing a simple harmonic motion. If $$\phi$$ represent the angle made by the magnet with the magnetic meridian, the moment of couple acting on the magnet is